{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying a FIR filter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to apply a FIR filter: convolve, fftconvolve, convolve1d or lfilter?\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "The following plot shows the time required to apply a finite impulse\n",
    "response (FIR) filter of varying length to a signal of length 131072\n",
    "using several different functions that are available in numpy and scipy.\n",
    "The details of how this figure was created are given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dzfDhw+0qN9vQoUP57LPPSE5OBiArK4v33nuPBx54AICRI0dSpUoVDh06xM8/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\nPVegnv18+sBptq3Zxo61O9j7y15KnSlF7Sq1qVa6GmWyypCZm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uzPb1VKOmtE7PYUv1HH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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fc44898>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Details\n",
    "-----------\n",
    "\n",
    "There are several functions in the numpy and scipy libraries that can be\n",
    "used to apply a [FIR\n",
    "filter](http://en.wikipedia.org/wiki/Finite_impulse_response) to a\n",
    "signal. From scipy.signal, lfilter() is designed to apply a discrete\n",
    "[IIR filter](http://en.wikipedia.org/wiki/Infinite_impulse_response) to\n",
    "a signal, so by simply setting the array of denominator coefficients to\n",
    "[1.0], it can be used to apply a FIR filter. Applying a FIR filter is\n",
    "equivalent to a discrete\n",
    "[convolution](http://en.wikipedia.org/wiki/Convolution), so one can also\n",
    "use convolve() from numpy, convolve() or fftconvolve() from\n",
    "scipy.signal, or convolve1d() from scipy.ndimage. In this page, we\n",
    "demonstrate each of these functions, and we look at how the\n",
    "computational time varies when the data signal size is fixed and the FIR\n",
    "filter length is varied. We'll use a data signal length of 131072, which\n",
    "is 2\\*\\*17. We assume that we have *m* channels of data, so our input\n",
    "signal is an *m* by *n* array. For the one dimensional timing, we use use \n",
    "a source array the size of 2\\*10^4 with varying number of filter coefficients.\n",
    "\n",
    "We assume our FIR filter coefficients are in a one-dimensional array\n",
    "*b*. The function numpy.convolve only accepts one-dimensional arrays, so\n",
    "we'll have to use a python loop over our input array to perform the\n",
    "convolution over all the channels. One way to do that is\n",
    "\n",
    "    y = np.array([np.convolve(xi, b, mode='valid') for xi in x])\n",
    "\n",
    "We use a list comprehension to loop over the rows of *x*, and pass the\n",
    "result to *np.array* to reassemble the filtered data into a\n",
    "two-dimensional array. It should be noted that in the one-dimensional case,\n",
    "`scipy.signal.convolve` possibly uses `np.convolve`.\n",
    "\n",
    "Both `signal.convolve` and `signal.fftconvolve` perform a two-dimensional\n",
    "convolution of two-dimensional arrays. To filter our *m* by *n* array\n",
    "with either of these functions, we shape our filter to be a\n",
    "two-dimensional array, with shape 1 by *len(b)*. The python code looks\n",
    "like this:\n",
    "\n",
    "    y = convolve(x, b[np.newaxis, :], mode='valid')\n",
    "\n",
    "where *x* is a numpy array with shape *(m, n)*, and *b* is the\n",
    "one-dimensional array of FIR filter coefficients. *b[np.newaxis, :]* is\n",
    "the two dimensional view of *b*, with shape 1 by *len(b)*. *y* is the\n",
    "filtered data; it includes only those terms for which the full\n",
    "convolution was computed, so it has shape *(m, n - len(b) + 1)*.\n",
    "\n",
    "ndimage.convolve1d() is designed to do a convolution of a 1d array along\n",
    "the given axis of another n-dimensional array. It does not have the\n",
    "option mode='valid', so to extract the valid part of the result, we\n",
    "slice the result of the function:\n",
    "\n",
    "    y = convolve1d(x, b)[:, (len(b)-1)//2 : -(len(b)//2)]\n",
    "    \n",
    "signal.lfilter is designed to filter one-dimensional data. It can take a\n",
    "two-dimensional array (or, in general, an n-dimensional array) and\n",
    "filter the data in any given axis. It can also be used for IIR filters,\n",
    "so in our case, we'll pass in [1.0] for the denominator coefficients. In\n",
    "python, this looks like:\n",
    "\n",
    "    y = lfilter(b, [1.0], x)\n",
    "\n",
    "To obtain exactly the same array as computed by convolve or fftconvolve\n",
    "(i.e. to get the equivalent of the 'valid' mode), we must discard the\n",
    "beginning of the array computed by lfilter. We can do this by slicing\n",
    "the array immediately after the call to filter:\n",
    "\n",
    "    y = lfilter(b, [1.0], x)[:, len(b) - 1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following script computes and plots the results of applying a FIR\n",
    "filter to a 2 by 131072 array of data, with a series of FIR filters of\n",
    "increasing length."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#!python\n",
    "%matplotlib inline\n",
    "from __future__ import print_function\n",
    "import time\n",
    "\n",
    "import numpy as np\n",
    "from numpy import convolve as np_convolve\n",
    "from scipy.signal import fftconvolve, lfilter, firwin\n",
    "from scipy.signal import convolve as sig_convolve\n",
    "from scipy.ndimage import convolve1d\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Did np.convolve and lfilter produce the same results?\n",
      "Yes.\n",
      "Did fftconvolve and lfilter produce the same results?\n",
      "Yes.\n",
      "Did convolve1d and lfilter produce the same results?\n",
      "Yes.\n"
     ]
    }
   ],
   "source": [
    "# Create the m by n data to be filtered.\n",
    "m = 1\n",
    "n = 2 ** 18\n",
    "x = np.random.random(size=(m, n))\n",
    "\n",
    "conv_time = []\n",
    "npconv_time = []\n",
    "fftconv_time = []\n",
    "conv1d_time = []\n",
    "lfilt_time = []\n",
    "\n",
    "diff_list = []\n",
    "diff2_list = []\n",
    "diff3_list = []\n",
    "\n",
    "ntaps_list = 2 ** np.arange(2, 14)\n",
    "\n",
    "for ntaps in ntaps_list:\n",
    "    # Create a FIR filter.\n",
    "    b = firwin(ntaps, [0.05, 0.95], width=0.05, pass_zero=False)\n",
    "\n",
    "    # --- signal.convolve ---\n",
    "    tstart = time.time()\n",
    "    conv_result = sig_convolve(x, b[np.newaxis, :], mode='valid')\n",
    "    conv_time.append(time.time() - tstart)\n",
    "\n",
    "    # --- numpy.convolve ---\n",
    "    tstart = time.time()\n",
    "    npconv_result = np.array([np_convolve(xi, b, mode='valid') for xi in x])\n",
    "    npconv_time.append(time.time() - tstart)\n",
    "\n",
    "    # --- signal.fftconvolve ---\n",
    "    tstart = time.time()\n",
    "    fftconv_result = fftconvolve(x, b[np.newaxis, :], mode='valid')\n",
    "    fftconv_time.append(time.time() - tstart)\n",
    "\n",
    "    # --- convolve1d ---\n",
    "    tstart = time.time()\n",
    "    # convolve1d doesn't have a 'valid' mode, so we expliclity slice out\n",
    "    # the valid part of the result.\n",
    "    conv1d_result = convolve1d(x, b)[:, (len(b)-1)//2 : -(len(b)//2)]\n",
    "    conv1d_time.append(time.time() - tstart)\n",
    "\n",
    "    # --- lfilter ---\n",
    "    tstart = time.time()\n",
    "    lfilt_result = lfilter(b, [1.0], x)[:, len(b) - 1:]\n",
    "    lfilt_time.append(time.time() - tstart)\n",
    "\n",
    "    diff = np.abs(fftconv_result - lfilt_result).max()\n",
    "    diff_list.append(diff)\n",
    "\n",
    "    diff2 = np.abs(conv1d_result - lfilt_result).max()\n",
    "    diff2_list.append(diff2)\n",
    "\n",
    "    diff3 = np.abs(npconv_result - lfilt_result).max()\n",
    "    diff3_list.append(diff3)\n",
    "\n",
    "# Verify that np.convolve and lfilter gave the same results.\n",
    "print(\"Did np.convolve and lfilter produce the same results?\",)\n",
    "check = all(diff < 1e-13 for diff in diff3_list)\n",
    "if check:\n",
    "    print( \"Yes.\")\n",
    "else:\n",
    "    print( \"No!  Something went wrong.\")\n",
    "\n",
    "# Verify that fftconvolve and lfilter gave the same results.\n",
    "print( \"Did fftconvolve and lfilter produce the same results?\")\n",
    "check = all(diff < 1e-13 for diff in diff_list)\n",
    "if check:\n",
    "    print( \"Yes.\")\n",
    "else:\n",
    "    print( \"No!  Something went wrong.\")\n",
    "\n",
    "# Verify that convolve1d and lfilter gave the same results.\n",
    "print( \"Did convolve1d and lfilter produce the same results?\",)\n",
    "check = all(diff2 < 1e-13 for diff2 in diff2_list)\n",
    "if check:\n",
    "    print( \"Yes.\")\n",
    "else:\n",
    "    print( \"No!  Something went wrong.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def timeit(fn, shape, lfilter=False, n_x=2e4, repeats=3):\n",
    "    x = np.random.rand(int(n_x))\n",
    "    y = np.random.rand(*shape)\n",
    "    args = [x, y] if not lfilter else [x, x, y]\n",
    "    times = []\n",
    "    for _ in range(int(repeats)):\n",
    "        start = time.time()\n",
    "        c = fn(*args)\n",
    "        times += [time.time() - start]\n",
    "    return min(times)\n",
    "    \n",
    "npconv_time2, conv_time2, conv1d_time2 = [], [], []\n",
    "fftconv_time2, sig_conv_time2, lconv_time2 = [], [], []\n",
    "Ns_1d = 2*np.logspace(0, 4, num=11, dtype=int)\n",
    "for n in Ns_1d:\n",
    "    npconv_time2 += [timeit(np_convolve, shape=(n,))]\n",
    "    conv1d_time2 += [timeit(convolve1d, shape=(n,))]\n",
    "    fftconv_time2 += [timeit(fftconvolve, shape=(n,))]\n",
    "    sig_conv_time2 += [timeit(sig_convolve, shape=(n,))]\n",
    "    lconv_time2 += [timeit(lfilter, shape=(n,), lfilter=True)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Ad0+MEB8X48PHxDgJIUDcp1cnnJt1x98PuuN9qDveh/rB+1F3uuZmY+jTyxhjjDHGGGOM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xmXKBecJjoxef5k1p5dS2BoIPsG7uPFmroNfPo4GyS0T0V989PuAsOBlcDXgBQuV6JMlGX9x/HY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\nBb0iIiIiIiJSYSnoFRERERERkQrr/wEjsvS6CwwqEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e896f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(1, figsize=(16, 5.5))\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.loglog(ntaps_list, conv1d_time, 'k-p', label='ndimage.convolve1d')\n",
    "plt.loglog(ntaps_list, lfilt_time, 'c-o', label='signal.lfilter')\n",
    "plt.loglog(ntaps_list, fftconv_time, 'm-*', markersize=8, label='signal.fftconvolve')\n",
    "plt.loglog(ntaps_list[:len(conv_time)], conv_time, 'g-d', label='signal.convolve')\n",
    "plt.loglog(ntaps_list, npconv_time, 'b-s', label='numpy.convolve')\n",
    "plt.legend(loc='best', numpoints=1)\n",
    "plt.grid(True)\n",
    "plt.xlabel('Number of taps')\n",
    "plt.ylabel('Time to filter (seconds)')\n",
    "plt.title('Multidimensional timing')\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.loglog(Ns_1d, conv1d_time2, 'k-p', label='ndimage.convolve1d')\n",
    "plt.loglog(Ns_1d, lconv_time2, 'c-o', label='signal.lfilter')\n",
    "plt.loglog(Ns_1d, fftconv_time2, 'm-*', markersize=8, label='signal.fftconvolve')\n",
    "plt.loglog(Ns_1d, sig_conv_time2, 'g-d', label='signal.convolve')\n",
    "plt.loglog(Ns_1d, npconv_time2, 'b-s', label='np.convolve')\n",
    "plt.grid()\n",
    "plt.xlabel('Number of taps')\n",
    "plt.ylabel('Time to filter (seconds)')\n",
    "plt.title('One dimensional timing')\n",
    "plt.legend(loc='best')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot shows that, depending on the number of taps, either \n",
    "`numpy.convolve` or `scipy.signal.fftconvolve`/`scipy.signal.convolve` is the fastest.\n",
    "The above script can be used to explore variations of these results.\n",
    "\n",
    "It should be noted that `scipy.signal.convolve` makes a choice to use\n",
    "`scipy.signal.fftconvolve`, `np.convolve` or the convolve implementation found\n",
    "naturally in `scipy.signal.convolve` depending on the size/shape of the input arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
